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Helmholtz

Benchmarks

Task NameDataset NameSOTA ResultTrend
Higher-frequency wave-field predictionHelmholtz (test)
H1 Score0.422
32
Forward PDE solvingHelmholtz
Relative Error0.0072
26
PDE SolvingHelmholtz
RMSE (Helmholtz)0.222
17
Eigenvalue problem solvingHelmholtz Dimension: 6400 Precision: 1e-8
Average Computation Time (s)31.31
17
Forward PDE SolvingHelmholtz 10K-epoch
Relative L2 Error1
16
Learning PDEsHelmholtz 2D a=10
Relative L2 Error0
15
Solving PDEHelmholtz
Relative Error0.01
14
Physics-Informed PDE Solving2D Helmholtz (test)
Time (sec/iter)0.0228
14
Inverse PDE solvingHelmholtz full observations
Relative Error0.049
14
Forward PDE SolvingHelmholtz (test)
Relative H1 Error0.1385
12
Spatio-temporal PDE reconstructionHelmholtz
PDE Residual0.55
12
PDE ReconstructionHelmholtz synthetic (test)
RMSE0.022
10
PDE ReconstructionHelmholtz 3% uniformly random measurements
Coefficient Relative L2 Error7.67
10
Inverse PDE solvingHelmholtz
Relative Error15.91
10
Neural Operator Learningδ-Helmholtz
Relative L2 Error0.0013
9
Forward PDE solvingHelmholtz Full Observation
L2 Relative Error0.0108
9
Inverse problemHelmholtz
PDE Residual0.2
9
Forward prediction2D Helmholtz
Relative L1 Error1.71
8
Shape Optimization and InversionHelmholtz
Inference Time (ms)0.47
8
PDE Inverse ProblemHelmholtz Noisy
L2 Relative Error67.93
7
PDE Forward ProblemHelmholtz Noisy
L2 Relative Error16.84
7
Inverse PDE SolvingHelmholtz
Relative L2 Error0.12
6
Forward PDE SolvingHelmholtz
Relative L2 Error0.025
6
Conditional source inferenceHelmholtz 256 samples (test)
Relative L2 Error0.381
6
Operator Learning for PDEsHelmholtz (downstream)
EG Score78.3
6
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